A search for charginos nearly mass-degenerate with the lightest supersymmetric particle is performed using the 176 pb−1 of data collected at 189 GeV in 1998 with the L3 detector. Mass differences between the chargino and the lightest supersymmetric particle below 4 GeV are considered. The presence of a high transverse momentum photon is required to single out the signal from the photon-photon interaction background. No evidence for charginos is found and upper limits on the cross section for chargino pair production are set. For the first time at LEP2, in the case of heavy scalar leptons, chargino mass limits are obtained for anyX ±/L-X 0/L mass difference.